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Low-cost, non-empirical corrections to semi-local density functional theory are essential for accurately modeling transition-metal chemistry. Here, we demonstrate the judiciously modified density functional theory (jmDFT) approach with non-empirical U and J parameters obtained directly from frontier orbital energetics on a series of transition-metal complexes. We curate a set of nine representative Ti(III) and V(IV) d 1 transition-metal complexes and evaluate their flat-plane errors along the fractional spin and charge lines. We demonstrate that while jmDFT improves upon both DFT+U and semi-local DFT with the standard atomic orbital projectors (AOPs), it does so inefficiently. We rationalize these inefficiencies by quantifying hybridization in the relevant frontier orbitals. To overcome these limitations, we introduce a procedure for computing a molecular orbital projector (MOP) basis for use with jmDFT. We demonstrate this single set of d 1 MOPs to be suitable for nearly eliminating all energetic delocalization and static correlation errors. In all cases, MOP jmDFT outperforms AOP jmDFT, and it eliminates most flat-plane errors at non-empirical values. Unlike DFT+U or hybrid functionals, jmDFT nearly eliminates energetic delocalization and static correlation errors within a non-empirical framework. 

Understanding how to control the nucleation and growth rates is crucial for designing nanoparticles with specific sizes and shapes. In this study, we show that the nucleation and growth rates are correlated with the thermodynamics of metal–ligand/solvent binding for the pre-reduction complex and the surface of the nanoparticle, respectively. To obtain these correlations, we measured the nucleation and growth rates by in situ small angle X-ray scattering during the synthesis of colloidal Pd nanoparticles in the presence of trioctylphosphine in solvents of varying coordinating ability. The results show that the nucleation rate decreased, while the growth rate increased in the following order, toluene, piperidine, 3,4-lutidine and pyridine, leading to a large increase in the final nanoparticle size (from 1.4 nm in toluene to 5.0 nm in pyridine). Using density functional theory (DFT), complemented by 31 P nuclear magnetic resonance and X-ray absorption spectroscopy, we calculated the reduction Gibbs free energies of the solvent-dependent dominant pre-reduction complex and the solvent-nanoparticle binding energy. The results indicate that lower nucleation rates originate from solvent coordination which stabilizes the pre-reduction complex and increases its reduction free energy. At the same time, DFT calculations suggest that the solvent coordination affects the effective capping of the surface where stronger binding solvents slow the nanoparticle growth by lowering the number of active sites (not already bound by trioctylphosphine). The findings represent a promising advancement towards understanding the microscopic connection between the metal–ligand thermodynamic interactions and the kinetics of nucleation and growth to control the size of colloidal metal nanoparticles. 

Metal nanoparticles have received substantial attention in the past decades for their applications in numerous areas, including medicine, catalysis, energy, and the environment. Despite these applications, the fundamentals of adsorption on nanoparticle surfaces as a function of nanoparticle size, shape, metal composition, and type of adsorbate are yet to be found. Herein, we introduce the first universal adsorption model that accounts for detailed nanoparticle structural characteristics, metal composition, and different adsorbates by combining first principles calculations with machine learning. Our model fits a large number of data and accurately predicts adsorption trends on nanoparticles (both monometallic and alloy) that have not been previously seen. In addition to its application power, the model is simple and uses tabulated and rapidly calculated data for metals and adsorbates. We connect adsorption with stability behavior of nanoparticles, thus advancing the design of optimal nanoparticles for applications of interest, such as catalysis. 

Small nanoparticles, a.k.a. nanoclusters, of transition metals have been studied extensively for a wide range of applications due to their highly tunable properties dependent on size, structure, and composition. For these small particles, there has been considerable effort towards theoretically predicting what is the most energetically favorable arrangement of atoms when forming a nanocluster. In this work, we develop a computational framework that couples density-functional theory calculations with mathematical optimization modeling to identify highly stable, mono-metallic transition metal nanoclusters of various sizes. This is accomplished by devising and solving a rigorous mathematical optimization model that maximizes a general cohesive energy function to obtain nanocluster structures of provably maximal cohesiveness. We then utilize density-functional theory calculations and error term regression to identify model corrections that are necessary to account with better accuracy for different transition metals. This allows us to encode metal-specific, analytical functions for cohesive energy into a mathematical optimization-based framework that can accurately predict which nanocluster geometries will be most cohesive according to density-functional theory calculations. We employ our framework in the context of Ag, Au, Cu, Pd and Pt, and we present sequences of highly cohesive nanoclusters for sizes up to 100 atoms, yielding insights into structures that might be experimentally accessible and/or structures that could be used as model nanoclusters for further study.